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Consider the following chart of student enrollment at a particular college. Arts & Sc. Engineering Business Total Females 2500 1070 550 4120 Males 2100 1350 630 4080 Total 4600 2420 1180 8200 A student is picked randomly. Let . E represent the event that an engineering student is selected, A = Arts and Sciences student, B = Business student, . M = Male and F = Female student. A single student is selected at random from this college: a. Express the event that the student picked is a Male student in Art and Sciences ( in terms of A, B, E, M, F). b. Find the probability of that event. c. Find P(A), and P(M). d. Are the events A and M independent? Explain. K e. Find the conditional probability that the student is a Male given that he/she is in Arts and Sciences.A study of book reviews in American Literature was published in Washington Post. The overall rating stated in each review was ascertained and recorded as follows: 1 = would not recommend, 2 = very little recommendation, 3 = no preference, 4 = recommended and 5 = outstanding contribution. The probability distribution of rating, X, is: X | p(x) -- 0.08 2 0.15 W 0.24 4 [ ??? 5 | 0.14 a) What is the probability that a randomly chosen book will have recommended (4) or higher rating. b) Suppose two books are chosen randomly, what is the probability that at least one of them have recommended or higher rating. c) What is the Expected rating - MU